Remember the origin of the pig squeal: it's the vocalization of a pig on its way to slaughter. Give the pig squeal or bree its due.
Practice breathing in deeply as you work on doing a pig squeal or bree, and add a raspy sound to your inhalation as you do so. Think of having an asthma attack, or walking into a room full of cats when you're allergic to them and you have the right idea. As you get that down, add an "oo," "ee," or some other vowel sound with your lips, your tongue, the position of your mouth or all three in combination.
Work on breathing in rather forcefully while you do step two, and add a squeal to the sound. Think of sucking on a straw and squealing at the same time. With some work, you'll get a nice, high-pitched pig squeal or bree.
Attempt to add more of a sound to your pig squeal like "bree" or "quee." Just be careful, though, as you're doing this, because you could damage your throat. Stop the instant your throat feels a little scratchy and work on doing the pig squeal without pain.
Do the above steps over and over and you will find that your vocal chords develop and grow stronger, enabling you to do a passable pig squeal or bree. Doing a pig squeal with the microphone helps as you do the squeal, and it saves you from trying to strain your vocal chords too much.